An Australian journalist who is being held in an Egyptian jail has described his detention as an "attack on freedom of speech" in letters to his family.

Peter Greste and two colleagues working for al-Jazeera were arrested on 30 December for allegedly holding illegal meetings with the banned Muslim Brotherhood. He said in his letters the detention had not led him to being charged formally, "much less convicted of any crime".

Greste, 48, a former BBC correspondent, sent the letters from Tora prison in Cairo where he said he had his first walk in the "weak winter sunshine" after spending 10 days being locked in his cell 24 hours a day when not being questioned.

He said he feared writing might result in harsh treatment. One letter said: "I am nervous as I write this. I am in my cold prison cell after my first official exercise session – four glorious hours in the grass yard behind our block and I don't want that right to be snatched away."

He said he had changed his mind about remaining silent about his detention despite risking having his books and pen taken from him. "I want to protect them almost as much as I want my freedom back. That is why I have sought, until now, to fight my imprisonment quietly from within, to make the authorities understand that this is all a terrible mistake, that I've been caught in the middle of a political struggle that is not my own. But after two weeks in prison it is now clear that this is a dangerous decision. It validates an attack not just on me and my two colleagues but on freedom of speech across Egypt. All of a sudden, my books seem rather petty."

He had been in the capital Cairo for just three weeks before he was arrested along with a fellow journalist, Mohamed Fahmy, and cameraman Baher Mohamed.

"We had been doing exactly as any responsible, professional journalist would – recording and trying to make sense of the unfolding events with all the accuracy, fairness and balance that our imperfect trade demands."

His colleagues, he wrote, were being held in worse conditions than he was. "Fahmy and Baher have been accused of being MB members, so they are being held in the far more draconian 'Scorpion prison' built for convicted terrorists. Fahmy has been denied the hospital treatment he badly needs for a shoulder injury he sustained shortly before our arrest. Both men spend 24 hours a day in their mosquito-infested cells, sleeping on the floor with no books or writing materials to break the soul-destroying tedium.

He thanked his family for their campaign to get him released and those who had written letters and posted online in his support.

"All of it has been both humbling and empowering. We know we are not alone. But what is galling is that we are into our fourth week behind bars for what I consider to be some pretty mundane reporting.

"I've produced work in the past that has involved lots of detailed investigation, considerable risk, and not a small amount of sweat, that I wished the authorities would have been even a little bit offended by. Yet too often it has slipped out with infuriatingly little response.

"This assignment to Cairo had been relatively routine – an opportunity to get to know Egyptian politics a little better.

"This is not a trivial point. The fact that we were arrested for what seems to be a set of relatively uncontroversial stories tells us a lot about what counts as 'normal' and what is dangerous in post-revolutionary Egypt."